The Demotion of Gauge Field Theory, the Theoretical Reconstruction of the Standard Model, and the Five-Layer Axiomatization Structure — Precursor Cascade Asymmetry, the Regime Function of the Higgs Mechanism, the Statistical Correspondence of Virtual States, and the Final Formalization of the Factor Hierarchy Law (IV)

Abstract

This paper is the concluding piece of the regime audit series on the Standard Model of particle physics, completing three core missions. First, it completes the demotion of gauge field theory — demonstrating that gauge field theory is not the most fundamental framework but rather the expression of regime boundaries in the language of group theory. The Factor Hierarchy Law is a deeper organizing principle than gauge field theory. Second, using regime boundary theory, it completes the theoretical reconstruction of the Standard Model. The statistical origin of CP violation lies in precursor cascade asymmetry — the cascade asymmetry between the strange→charm deviation of 0.0052 GeV and the charm→bottom deviation of 0.0000 GeV constitutes the statistical definition of symmetry breaking within the Chow test framework. Cascade asymmetry may be reactivated at cascade pairs that cross switching-type boundaries, with its complete verification requiring measurement of the bottom→top cascade deviation. The essential function of the Higgs mechanism is to generate regime boundaries — it partitions a continuous mass spectrum into discrete regime centers. Virtual intermediate states are the quantum expression of precursor signals. Third, based on all empirical findings from the previous three papers, it extracts directly usable mathematical assets — the charm-region piecewise decay equation, the bottom-region piecewise decay equation, the formalized expression of the precursor cascade, the universal formula for transition zone widths, and the intercept/slope ratio criterion for switching types. Fourth, it formalizes the entire theoretical system into a five-layer axiomatization structure — law layer, norm layer, algorithm layer, theorem-and-proposition layer, and theory layer — and proposes five testable predictions. Fifth, it completes the full audit of the Factor Hierarchy Law in the Standard Model of particle physics — a complete closed loop from empirical discovery to mathematical theorem to theoretical derivation to system architecture. Research Paradigm Statement: The core methodology, research direction, and final decisions were independently directed by the author. DeepSeek assisted with code implementation, data presentation, and text drafting. The author takes full academic responsibility for the final content.